agenda october 23, 2012 hand in homework new unit homework time

AGENDA OCTOBER 23, 2012 HAND IN HOMEWORK New Unit Homework time

Students will solve and graph one-step linear inequalities.

Objectives

INDENTIFY

Warm UpSolve each equation. 1. –5a = 30 2.

Graph each inequality.

5. x ≥ –10

6. x < –3

–6 –10

3. 4.

Real World - InequalityOBTAIN

Other ways You must be at least 42” to ride the roller coaster You must be in bed by 9 Your GPA must have at least a 2.0 to play sports You can have at most 2 pieces of luggage

New: MIX –FREEZE –PAIR

What are some other examples?

VOCAB -Review of Inequality Signs

> greater than< less than< less than

greater than or equal

less than or equal

Remember, solving inequalities is similar to solving equations. To solve an inequality that contains multiplication or division, undo the operation by dividing or multiplying both sides of the inequality by the same number.

The following rules show the properties of inequality for adding or subtracting and multiplying or dividing by a positive number. The rules for multiplying or dividing by a negative number appear later in this lesson.

REMEMBER UNIT 1 – PREVIOUS CONNECTION

d – 5 > –7

Since 5 is subtracted from d, add 5 to both sides to undo the subtraction.

Draw an empty circle at –2.

Shade all numbers greater than –2 and draw an arrow pointing to the right.

+5 +5d + 0 > –2

d > –2

d – 5 > –7

Solve the inequality and graph the solutions.

–10 –8 –6 –4 –2 0 2 4 6 8 10

I DO


x + 12 < 20 x + 12 < 20

–12 –12x + 0 < 8

x < 8

Since 12 is added to x, subtract 12 from both sides to undo the addition.

–10 –8 –6 –4 –2 0 2 4 6 8 10Draw an empty circle at 8.

Shade all numbers less than 8 and draw an arrow pointing to the left.

WE DO

Writing MathWhy can the solutions of 3+x < 9 can be written in set notation

and as “the set of all real numbers X such that x is less than six?”

How do you decide on which way to shade the graph?

Why is it important to test variables that are positive, negative, and zero?

ON A STICKY NOTE – WRITE DOWN YOUR ANSWER THEN WE WILL SHARE

Apply / Evaluate

OBTAIN

Check It Out! I DO


4k > 24

k > 6

0 2 4 6 8 10 12 16 18 2014

Since k is multiplied by 4, divide both sides by 4.


7x > –42

7x > –42

>

1x > –6

Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.

x > –6

–10 –8 –6 –4 –2 0 2 4 6 8 10

WE DO

r < 16

0 2 4 6 8 10 12 14 16 18 20

Since r is multiplied by ,

multiply both sides by the

reciprocal of .

WE DO


Since x is divided by –3, multiply both sides by –3. Change to .

16 18 20 22 2410 14 26 28 3012


24 x (or x 24)

I DO

–50 ≥ 5q

–10 ≥ q

Since q is multiplied by 5, divide both sides by 5.

Check It Out! We Do


5–5 0–10–15 15

Caution!

Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24.


–12x > 84

x < –7

Since x is multiplied by –12, divide both sides by –12. Change > to <.

–10 –8 –6 –4 –2 0 2 4 6–12–14

–7

YOU DO- CHECK

Solve each inequality and graph the solutions.

a. 10 ≥ –x

–1(10) ≤ –1(–x)

–10 ≤ x

Multiply both sides by –1 to make x positive. Change to .

–10 –8 –6 –4 –2 0 2 4 6 8 10

HARD ONE – YOU DO


Objectives

Lesson QuizSolve each inequality and graph the solutions.

1. X + 4 < 1 x < –3 2. –5x ≥ 30 x ≤ –6

3. x > 20 4. x ≥ 6

5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy?0, 1, 2, 3, 4, 5, 6, or 7 shirts

CHECK FOR MASTERY

TIC TAC TOE


Objectives

On Your Objective Page – Rate Yourself

What if…? Josh wants to try to break the school bench press record of 282 pounds. He currently can bench press 250 pounds. Write and solve an inequality to determine how many more pounds Josh needs to lift to break the school record. Check your answer.

Let p represent the number of additional pounds Josh needs to lift.

250 pounds plus additional pounds is greater than

282 pounds.

250 + p > 282

Example 3: Application

$4.30 times number of tubes is at most $20.00.

4.30 • p ≤ 20.00

Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy?

Let p represent the number of tubes of paint that Jill can buy.

4.30p ≤ 20.00

p ≤ 4.65…

Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change.

Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint.

Example 3 Continued

Check It Out!

A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill?

10 oz timesnumber of servings

is at most 128 oz

10 • x ≤ 128

Let x represent the number of servings of juice the pitcher can contain.

Check It Out!

10x ≤ 128

Since x is multiplied by 10, divide both sides by 10.

The symbol does not change.

x ≤ 12.8

The pitcher can fill 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 servings.


Objectives

On your objective page – rate yourself!! Now apply knowledge HOMEWORK

agenda october 23, 2012 hand in homework new unit homework time

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